FAST Hypothesis Testing 3 — Questions and Answers
Question 1: Which factor does NOT directly increase the power of a hypothesis test?
- Increasing sample size
- Increasing effect size
- Raising the significance level α (Correct answer)
- Decreasing the standard deviation
Correct answer: Raising the significance level α
Raising α increases power but at the cost of a higher Type I error rate; reducing SD or increasing n/effect size raises power without that trade-off.
Question 2: A z-test is appropriate when:
- The population variance is unknown and n < 30
- The population variance is known or n is large (Correct answer)
- The data are categorical
- The distribution is heavily skewed
Correct answer: The population variance is known or n is large
A z-test is used when the population standard deviation is known or the sample size is large enough for the Central Limit Theorem to apply.
Question 3: What is a p-value?
- The probability that the null hypothesis is true
- The probability of observing a result at least as extreme as the sample result, assuming H₀ is true (Correct answer)
- The significance level chosen by the researcher
- The probability the alternative hypothesis is true
Correct answer: The probability of observing a result at least as extreme as the sample result, assuming H₀ is true
The p-value measures how likely the observed data (or more extreme) would be if the null hypothesis were true.
Question 4: In a paired t-test, what is being compared?
- Means of two independent groups
- Differences within the same subjects measured twice (Correct answer)
- Variances of two populations
- Proportions from two samples
Correct answer: Differences within the same subjects measured twice
A paired t-test analyzes the mean difference between two measurements taken on the same subject or matched pairs.
Question 5: A confidence interval for a mean does not include zero. What does this imply about the two-tailed hypothesis test at the matching α level?
- Fail to reject H₀: μ = 0
- Reject H₀: μ = 0 (Correct answer)
- More data are needed
- The test is one-tailed
Correct answer: Reject H₀: μ = 0
If zero falls outside the confidence interval, it means the null value is implausible, which corresponds to rejecting H₀ at the matching significance level.
Question 6: Which statement about the null hypothesis (H₀) is correct?
- It is what the researcher hopes to prove
- It always states there is no effect or no difference (Correct answer)
- It is accepted when p > α
- It is the same as the research hypothesis
Correct answer: It always states there is no effect or no difference
H₀ is the default assumption of no effect, no difference, or no relationship that the test attempts to refute.
Question 7: A researcher increases sample size from 50 to 200. Holding everything else constant, what happens to the standard error?
- It doubles
- It quadruples
- It is halved (Correct answer)
- It is quartered
Correct answer: It is halved
Standard error = σ/√n; quadrupling n (50→200) means √n doubles, so SE is halved.
FAST Hypothesis Testing 3
Which factor does NOT directly increase the power of a hypothesis test?